In the recent and important context of Nevanlinna-Pick interpolation theory for classes of holomorphic functions with constraints, see [4],[5], and [14], the starting point has been to describe the common invariant subspaces of the operators of multiplication by S2 and S3 on the Hardy classes. In the same spirit this paper offers as a new result the charcterization of the common invariant subspaces of S2 and S3 on the space BMOA. In addition we present a new, elementary and short proof of the invariant subspace characterization of the operator S on BMOA and use this to give a new proof of the invariant subspace characterization of the backward shift on the Hardy space H1 that is also short and elementary. © 2014 University of Houston.